I am descended from Frederick William Hoysted (1818 - 1901), who emigrated to Australia with his wife and nine children in 1859. He and his descendants in Australia (often known as the "horsey Hoysteds" due to their association with horse racing over several generations) have been extensively researched, and were the subject of a book by Una Richards, published for a family reunion in the late 1980s.
There are a number of Frederick William Hoysteds. They appear to be named after Lt Colonel Frederick William Hoysted, who served in the British Army in the American War of Independence and the Napoleonic wars. Lt Col Frederick William Hoysted died in the same year - 1818 - that the Frederick William who came to Australia in 1859 was born. You may speculate on a connection if you wish!